Multiple correspondence analysis (MCA) is formulated by various approaches, and homogeneity analysis (HA) is a major one among them. However, the HA approach has not yet provided a suitable index of GOF (goodness-of-fit) of multidimensional solutions. In this paper, the use of a correct classification rate (CCR) as the index is considered. We argue that CCR is congruous to the homogeneity assumption underlying HA, to justify the use of CCR in HA. Following this, we perform a simulation study to evaluate CCR by comparing it with eigenvalue-based GOF indices which have been derived from another approach to MCA. In the simulation CCR showed better performance than the eigenvalue-based indices: the former was found useful for evaluating the quality of MCA solutions and choosing solutions of proper dimensionalities. CCR also gave reasonable results in real data examples

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Interval data may appear in perturbed problems or when measured quanties are subject to error. Small errors in data also occur because of roundoff. We have used interval analysis to bound data values and their arithmetic solutions. An algorithm that uses the interval quadratic and Newton methods to enclose minimum values is used in a least-squares objective function. As a result, appropriate bounds for the coefficient of a regression model have been obtained. An example from cardiology in Billard and Diday (2000) is illustrated.

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The Cox regression model is often used to evaluate effects of covariates on failure time distributions for competing risks survival data. We consider a situation where failure times are observed but failure types cannot be observed for some individuals, assuming that the probability of missing the type of a failure is identical for all failure types. Hemmi (1995) has proposed a maximum pseudo-partial likelihood estimator (MPPLE) of regression coefficients in the Cox model in order to improve the maximum partial likelihood estimator (MPLE). The MPPLE has consistency, but its distribution, which is required for interval estimation, has not analytically been obtained so far. This paper applies bootstrap methods such as the percentile and BCa methods to construct confidence intervals for the regression coefficients based on the MPPLE, and evaluates them numerically in terms of coverage probability and interval length. Simulation studies show that the bootstrap methods enable us to construct appropriate confidence intervals, and that the bootstrap confidence intervals based on the MPPLE are shorter than the confidence intervals given by the normal approximation based on the MPLE.

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Simultaneous confidence intervals for pairwise multiple comparisons among mean vectors under elliptical populations are considered. The estimation of simultaneous confidence intervals is given by using the approximate upper percentiles of the T²_max statistic based on Bonferroni's inequality. In order to obtain the upper percentiles of the T²_max statistic, an asymptotic expansion for Hotelling's T²-type statistic under elliptical distributions is derived by the perturbation method. The accuracy and conservativeness of the approximations are evaluated via a Monte Carlo simulation study.

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